Some hypothesis tests for the covariance matrix when the dimension is large compared to the sample size

This paper analyzes whether standard covariance matrix tests work whendimensionality is large, and in particular larger than sample size. Inthe latter case, the singularity of the sample covariance matrix makeslikelihood ratio tests degenerate, but other tests based on quadraticforms of sample covariance matrix eigenvalues remain well-defined. Westudy the consistency property and limiting distribution of these testsas dimensionality and sample size go to infinity together, with theirratio converging to a finite non-zero limit. We find that the existingtest for sphericity is robust against high dimensionality, but not thetest for equality of the covariance matrix to a given matrix. For thelatter test, we develop a new correction to the existing test statisticthat makes it robust against high dimensionality.

Honey, I shrunk the sample covariance matrix

The central message of this paper is that nobody should be using the samplecovariance matrix for the purpose of portfolio optimization. It containsestimation error of the kind most likely to perturb a mean-varianceoptimizer. In its place, we suggest using the matrix obtained from thesample covariance matrix through a transformation called shrinkage. Thistends to pull the most extreme coefficients towards more central values,thereby systematically reducing estimation error where it matters most.Statistically, the challenge is to know the optimal shrinkage intensity,and we give the formula for that. Without changing any other step in theportfolio optimization process, we show on actual stock market data thatshrinkage reduces tracking error relative to a benchmark index, andsubstantially increases the realized information ratio of the activeportfolio manager.

Exact and approximate stepdown methods for multiple hypothesis testing

Consider the problem of testing k hypotheses simultaneously. In this paper,we discuss finite and large sample theory of stepdown methods that providecontrol of the familywise error rate (FWE). In order to improve upon theBonferroni method or Holm's (1979) stepdown method, Westfall and Young(1993) make eective use of resampling to construct stepdown methods thatimplicitly estimate the dependence structure of the test statistics. However,their methods depend on an assumption called subset pivotality. The goalof this paper is to construct general stepdown methods that do not requiresuch an assumption. In order to accomplish this, we take a close look atwhat makes stepdown procedures work, and a key component is a monotonicityrequirement of critical values. By imposing such monotonicity on estimatedcritical values (which is not an assumption on the model but an assumptionon the method), it is demonstrated that the problem of constructing a validmultiple test procedure which controls the FWE can be reduced to the problemof contructing a single test which controls the usual probability of a Type 1error. This reduction allows us to draw upon an enormous resamplingliterature as a general means of test contruction.

Resurgence of HIV infection among men who have sex with men in Switzerland: mathematical modelling study.

BACKGROUND: New HIV infections in men who have sex with men (MSM) have increased in Switzerland since 2000 despite combination antiretroviral therapy (cART). The objectives of this mathematical modelling study were: to describe the dynamics of the HIV epidemic in MSM in Switzerland using national data; to explore the effects of hypothetical prevention scenarios; and to conduct a multivariate sensitivity analysis. METHODOLOGY/PRINCIPAL FINDINGS: The model describes HIV transmission, progression and the effects of cART using differential equations. The model was fitted to Swiss HIV and AIDS surveillance data and twelve unknown parameters were estimated. Predicted numbers of diagnosed HIV infections and AIDS cases fitted the observed data well. By the end of 2010, an estimated 13.5% (95% CI 12.5, 14.6%) of all HIV-infected MSM were undiagnosed and accounted for 81.8% (95% CI 81.1, 82.4%) of new HIV infections. The transmission rate was at its lowest from 1995-1999, with a nadir of 46 incident HIV infections in 1999, but increased from 2000. The estimated number of new infections continued to increase to more than 250 in 2010, although the reproduction number was still below the epidemic threshold. Prevention scenarios included temporary reductions in risk behaviour, annual test and treat, and reduction in risk behaviour to levels observed earlier in the epidemic. These led to predicted reductions in new infections from 2 to 26% by 2020. Parameters related to disease progression and relative infectiousness at different HIV stages had the greatest influence on estimates of the net transmission rate. CONCLUSIONS/SIGNIFICANCE: The model outputs suggest that the increase in HIV transmission amongst MSM in Switzerland is the result of continuing risky sexual behaviour, particularly by those unaware of their infection status. Long term reductions in the incidence of HIV infection in MSM in Switzerland will require increased and sustained uptake of effective interventions.

Improved estimation of the covariance matrix of stock returns with an application to portofolio selection

This paper proposes to estimate the covariance matrix of stock returnsby an optimally weighted average of two existing estimators: the samplecovariance matrix and single-index covariance matrix. This method isgenerally known as shrinkage, and it is standard in decision theory andin empirical Bayesian statistics. Our shrinkage estimator can be seenas a way to account for extra-market covariance without having to specifyan arbitrary multi-factor structure. For NYSE and AMEX stock returns from1972 to 1995, it can be used to select portfolios with significantly lowerout-of-sample variance than a set of existing estimators, includingmulti-factor models.

Flexible multivariate GARCH modeling with an application to international stock markets

The goal of this paper is to estimate time-varying covariance matrices.Since the covariance matrix of financial returns is known to changethrough time and is an essential ingredient in risk measurement, portfolioselection, and tests of asset pricing models, this is a very importantproblem in practice. Our model of choice is the Diagonal-Vech version ofthe Multivariate GARCH(1,1) model. The problem is that the estimation ofthe general Diagonal-Vech model model is numerically infeasible indimensions higher than 5. The common approach is to estimate more restrictive models which are tractable but may not conform to the data. Our contributionis to propose an alternative estimation method that is numerically feasible,produces positive semi-definite conditional covariance matrices, and doesnot impose unrealistic a priori restrictions. We provide an empiricalapplication in the context of international stock markets, comparing thenew estimator to a number of existing ones.

Repartición de los recursos alimenticios entre tres peces bentófagos frente al Perú antes, durante y después de El Niño 1982-83.

Se revisa la utilización de recursos alimenticios de tres peces bentófagos en los fondos arenosos someros de la Bahía de Ancón: Menticirrhus ophicephalus, stellifer minos y Paralichthys adspersus.

Subsampling inference in threshold autoregressive models

This paper discusses inference in self exciting threshold autoregressive (SETAR)models. Of main interest is inference for the threshold parameter. It iswell-known that the asymptotics of the corresponding estimator depend uponwhether the SETAR model is continuous or not. In the continuous case, thelimiting distribution is normal and standard inference is possible. Inthe discontinuous case, the limiting distribution is non-normal and cannotbe estimated consistently. We show valid inference can be drawn by theuse of the subsampling method. Moreover, the method can even be extendedto situations where the (dis)continuity of the model is unknown. In thiscase, also the inference for the regression parameters of the modelbecomes difficult and subsampling can be used advantageously there aswell. In addition, we consider an hypothesis test for the continuity ofthe SETAR model. A simulation study examines small sample performance.

Una retrospectiva a El Niño 1982-83: ¿qué hemos aprendido?

El "Niño del siglo" 1982-83, debido a sus peculiaridades inesperadas, sorprendió fuertemente a la comunidad científica. Como consecuencia, incluso en las ciencias biológicas marinas, donde los efectos fueron drásticos y a menudo obvios, en general se colectó menos información de lo que hubiera sido posible y deseable. De este panorama hay algunas excepciones, principalmente en lo referente al estudio de las comunidades bénticas y costeras. La reciente información acumulada en estos campos forma la base para una evaluación crítica del avance científico durante y después del fenómeno. Al mismo tiempo permite la ubicación de problemas y la formulación de proyectos de investigación para el futuro. Si bien es evidente que en este momento ya disponemos de una visión más clara de los efectos inmediatos, sean positivos o negativos, de un fenómeno extraordinariamente fuerte, la incertidumbre ante un nuevo El Niño mucho más tenue en 1986-87, nos dió una lección que hay que evaluar. Por otro lado, se ha avanzado muy poco en el estudio de los mecanismos que desencadenan elevadas mortandades de algunas especies y la proliferación inusual de otras. Sin embargo, ya tenemos alguna visión más integral sobre el efecto latitudinal, la gradiente vertical, los efectos previos a la llegada de las ondas Kelvin, los efectos post-Niño y los efectos de largo plazo. No obstante, hasta el momento, sólo podemos hipotetizar tanto sobre la historia evolutiva de El Niño, como sobre su significancia para el origen de las comunidades marinas del presente. Las investigaciones futuras deben tener un enfoque multidisciplinario, sin descuidar los aspectos básicos. Esto debería implicar: un mayor esfuerzo de las universidades a lo largo del litoral pacífico; investigaciones más continuadas; trabajos experimentales comparativos en diferentes lugares, a fin de saber más sobre los mecanismos involucrados; una mayor cooperación entre los científicos que trabajan en comunidades y problemas semejantes de las diversas latitudes; y un mayor intercambio de información entre los investigadores de comunidades actuales, paleontólogos, sedimentólogos y arqueólogos. Se concluye que sin duda hemos aprendido algo durante El Niño 1982-83; sin embargo, estaríamos aprovechando muy poco si no aceptamos nuestro reto de continuar profundizando estas investigaciones.

Modificaciones producidas durante "El Niño" en la infauna bentónica de áreas someras del ecosistema de afloramiento peruano

Analisis de los cambios del macrobentos a lo largo de transectos realizados periódicamente desde 1976 a 1983 en las diversas playas arenosas del departamento de Lima.

Cambios de los factores ambientales, macrobentos y bacterias filamentosas en la zona de mínimo de oxígeno frente al Perú durante "El Niño" 1982-1983

Analisis de los cambios de la biomasa y densidad de los diferentes grupos del macrobentos.

Incidencia del fenómeno El Niño sobre los mariscos en el litoral peruano

Estudio en base a la información acumulada en varias encuestas realizadas a los pescadores y de observaciones propias. Como material de contraste se han empleado los datos de IMARPE para la zona de Pisco.

Cambios en los Recursos Costeros y su Incidencia en la Pesquería Artesanal durante «El Niño» 1982 - 1983

Los efectos del intenso fenómeno «El Niño» (EN) en verano y otoño del año 1983 sobre la pesquería artesanal se estudiaron a través de viajes de inspección a 21 centros de desembarque a lo largo del litoral peruano, entre enero y julio. Los resultados se basan en encuestas, estadísticas, datos e informaciones obtenidas durante los viajes. El fuerte calentamiento del mar ad­yacente a la costa peruana ha determinado en las capturas el reemplazo de especies típicas como cabrilla, cachema, lenguado, pejerrey, loma, jurel, caballa y suco por especies de aguas tropicales como el dorado, sierra, picuda, barrilete, rayas, manta rayas y langostinos. Los desembarques de las especies tradicionales han disminuido alrededor de 40 % con respecto a los meses de enero a julio de años normales, alcanzando en Santa Rosa, Lomas, Chala y Meca hasta un 80 % de disminución. En el verano de 1983, las capturas promedio de las embarcaciones artesanales en el litoral norte fueron <400 kg por embarcación-viaje, cantidad 3 veces menor a las capturas del verano anterior, mientras que para el litoral sur fueron en promedio < 170 kg, es decir más de 4 veces menor que antes.

Hymenoepimecis neotropica (Brues & Richardson) (Hymenoptera, Ichneumonidae, Pimplinae) parasitoid of Araneus omnicolor (Keyserling) (Araneae, Araneidae): first host record and new occurrence to Brazil

Hymenoepimecis neotropica (Brues & Richardson) (Hymenoptera, Ichneumonidae, Pimplinae) parasitoid of Araneus omnicolor (Keyserling) (Araneae, Araneidae): first host record and new occurrence to Brazil. The species of the genus Hymenoepimecis occur only in Neotropical region, being recognized for using as their hosts spiders which build orbicular webs. That wasp was described occurring only in the Guyana. This work expands the geographical distribution of the species to Brazil and records the spider Araneus omnicolor (Araneae, Araneidae) as its host. Furthermore, it provides information about the natural history of this interaction.